A game involving chance is said to be a fair game if the expected amount won or lost is zero. Consider the following arcade game. A player pays $1 and chooses a number from 1 to 10. A spinning wheel then randomly selects a number from 1 to 10. If the numbers match, the player wins $5. Otherwise the player loses the $1 entry fee.
(a) Define a random variable W that is the amount won by the player and draw its probability distribution. (Capital letters other than X can be used for random variables.) Use negative values for losses, and positive values for winnings.
(b) Find the mean of W. Is this a fair game?